So at my session at Twitter Math Camp 12, I felt brave enough to admit to some of the questions I've found myself having as a non-native speaker of math teaching who walks among you. I confessed that they do not sound like the typical questions I feel are expected to be generated by students, although there are plenty of students in math classrooms who, like me, are non-native speakers.
The perplexing thing is, they generated a lot of interest and conversation about on-ramps for students into a state of flow while doing mathematical activity, so I thought I would make a list of them here. So without editing, here is a list of the questions I prepared as part of my thinking as I was working through the issues of flow for students to whom the physics-oriented world-around-us questions are not the most natural ones to raise.
I often look at Dan's digital media problems and set-ups and find myself wondering...
- Does it always work that way?
- Does it ever deviate?
- Are there any rules of thumb we can abstract from observing this process?
- Are there any exceptions? If so, what? If not, why not?
- How long have people known about this?
- Who first discovered this phenomenon?
- How was it useful to them in their context?
- How did they convince others it was an important aspect of the problem?
- Did the knowledge it represents ever get lost?
- If so, how/when was it rediscovered?
- How did this discovery cross culture? How did it cross between different fields of knowledge?
- What were the cultural barriers/obstacles to wider acceptance of these findings as knowledge?
- What were the implications of a culture accepting this knowledge?
- Why do I feel like the only person in the room who ever cares about these questions?
It also made me realize that I am not, in fact, alone.
You're definitely not alone. I'm right there with you on many of those questions. Especially "How was it useful to them in their context?"
ReplyDeleteExactly!!! The Babylonians used their geometric approach to solving quadratics as the foundation of their system of collecting appropriate taxes on farm lands and crop yields. And quadratics were essential to the complex system of medieval Islamic law codes, including women's rights in inheritance and divorce. That's one reason why Al-Kwarismi's consolidation of the rules of algebra into a single volume was considered so revolutionary: the Compendious Volume of Completion and Balancing eased the processes involved in trade, inheritance, surveying, and so many other human processes. Algebra is the study of BALANCE!
DeleteThat speaks to me more than the physics of a basketball going into a hoop.
Cool list. The first 4 are very much a mathematician's questions.
ReplyDeleteI found a LOT of the questions on this list to be mathematical. And in fact to be really awesome questions for teachers to ask of themselves/their subject to think about how to teach big ideas. Example: completing the square and the quadratic equation. They receive a lot of moaning, and so I'm really curious -- Who uses them? Who cares about them? Are there people who appreciate them and if so, why? Were there inventors proud? Did other people say "good on ya!" when they heard about their invention? Why?
ReplyDeleteI'm thrilled that Math Camp gave you space to articulate & share these questions -- I think we need to hear more questions like this and appreciate how mathematical they are.
Now I have some questions: how do you feel when these questions pop into your head now? How did you feel before math camp? Do you have any guesses about why they felt taboo? Do you have any guesses about what helped you feel comfortable enough to ask them?
Max — Good questions. I've been working on my own issues around this for a while, so I haven't worried what others thought about my own Qs for years now. However Twitter Math Camp was the first time I raised them in the context of raising other teachers' awareness that there are some of us out there who think differently about mathematics than others do and that this needs to be okay.
ReplyDeleteI think they felt taboo to me because there is a huge unspoken but very active culture of competition and shaming that underlies much of math education and mathematical activity in the U.S. I was never one of those students who was fast at mathematics, but I learned that when I gave myself space and support to do what I needed, I was capable of deep and rich mathematical practice.
I finally began to feel comfortable "coming out of the closet" about my feelings and questions when I started taking math classes again for the subject matter qualification part of my credential. I had a lot of amazing Russian professors who had been trained under the old Soviet system. They had a completely different perspective on what made a "good" math student than I had ever encountered before with American teachers. When *they* started encouraging me to push myself, to consider taking take advanced classes, and to consider doing graduate work in mathematics, I began to understand that there was nothing wrong with me or my own mind's way of understanding math — I just hadn't been speaking with teachers who understood my own understanding.
I still struggle with self-confidence and self-doubt when I do math (the Exeter sessions were grueling for me emotionally), but I've come to understand that that is simply a part of my process. It won't kill me, it won't even injure me, but it requires that I gather and encourage my own courage to do the work. And that gives me courage — and understanding — to encourage my students to find their own courage and not to give up on themselves.
As the great spiritual teacher A.H. Almaas says, "Struggling and wrestling is the process of understanding."